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Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input

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  • Liu, Meng
  • Wang, Ke

Abstract

Taking both white noises and colored noises into account, a stochastic single-species model with Markov switching and impulsive toxicant input in a polluted environment is proposed and investigated. Sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The threshold between weak persistence and extinction is obtained. Some simulation figures are introduced to illustrate the main results.

Suggested Citation

  • Liu, Meng & Wang, Ke, 2012. "Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1541-1550.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:12:p:1541-1550
    DOI: 10.1016/j.chaos.2012.08.011
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    References listed on IDEAS

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    1. Jiao, Jianjun & Ye, Kaili & Chen, Lansun, 2011. "Dynamical analysis of a five-dimensioned chemostat model with impulsive diffusion and pulse input environmental toxicant," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 17-27.
    2. Yang, Xiaofeng & Jin, Zhen & Xue, Yakui, 2007. "Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 726-735.
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    Cited by:

    1. Lan, Guijie & Wei, Chunjin & Zhang, Shuwen, 2019. "Long time behaviors of single-species population models with psychological effect and impulsive toxicant in polluted environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 828-842.
    2. Bashkirtseva, Irina & Ryashko, Lev & Ryazanova, Tatyana, 2019. "Stochastic variability and transitions to chaos in a hierarchical three-species population model," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 276-283.
    3. Li, Lijie & Feng, Yu & Liu, Yongjian, 2016. "Dynamics of the stochastic Lorenz-Haken system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 670-678.
    4. Slepukhina, E. & Ryashko, L. & Kügler, P., 2020. "Noise-induced early afterdepolarizations in a three-dimensional cardiac action potential model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Liu, Qun & Chen, Qingmei, 2015. "Dynamics of stochastic delay Lotka–Volterra systems with impulsive toxicant input and Lévy noise in polluted environments," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 52-67.

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